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arXiv:1405.5270 · Physical Review Letters

Two-Mode Thermal-Noise Squeezing in an Electromechanical Resonator

Imran Mahboob, Hajime Okamoto, Koji Onomitsu, Hiroshi Yamaguchi

Published Oct 17, 2014• 80 citations
arXivHTMLPDF

Abstract

An electromechanical resonator is developed in which mechanical nonlinearities can be dynamically engineered to emulate the nondegenerate parametric down-conversion interaction. In this configuration, phonons are simultaneously generated in pairs in two macroscopic vibration modes, resulting in the amplification of their motion. In parallel, two-mode thermal squeezed states are also created, which exhibit fluctuations below the thermal motion of their constituent modes as well as harboring correlations between the modes that become almost perfect as their amplification is increased. The existence of correlations between two massive phonon ensembles paves the way towards an entangled macroscopic mechanical system at the single phonon level.

DOI
10.1103/physrevlett.113.167203

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An electromechanical resonator is developed in which mechanical nonlinearities can be dynamically engineered to emulate the nondegenerate parametric down-conversion interaction. In this configuration, phonons are simultaneously generated in pairs in two macroscopic vibration modes, resulting in the amplification of their motion. In parallel, two-mode thermal squeezed states are also created, which exhibit fluctuations below the thermal motion of their constituent modes as well as harboring correlations between the modes that become almost perfect as their amplification is increased. The existence of correlations between two massive phonon ensembles paves the way towards an entangled macroscopic mechanical system at the single phonon level.
A mechanical resonator integrated with piezoelectric transducers enables mechanical nonlinearities to be dynamically engineered to emulate non-degenerate parametric down-conversion.In this configuration, millions of phonons are simultaneously generated in pairs in two macroscopic vibration modes, which results in the amplification of their motion by more than 20 dB.Mechanical two-mode squeezed states are also created in parallel, which exhibit fluctuations 5 dB below the thermal level of their constituent modes and they harbor correlations between the modes that become perfect as their amplification is increased.This remarkable observation of correlations between two massive phonon ensembles establishes the means to create an entangled macroscopic mechanical system at the single phonon level.
Two-mode squeezed states, generated via non-degenerate parametric down-conversion, are invariably revealed via their entangled vacuum or correlated thermal fluctuations. Here, two-mode thermal squeezed states, generated in an electromechanical system, are made bright by means of degenerate parametric amplification of their constituent modes to the point where they are almost perfect, even when seeded from low intensity non-degenerate parametric down-conversion. More dramatically, activating the degenerate parametric resonances of the underlying modes yields perfect correlations which can be resolved via the coordinated switching of their phase bi-stable vibrations, without recourse to monitoring their thermal fluctuations. This ability to enhance the two-mode squeezed states and to decipher them without needing to observe their intrinsic noise is supported by both analytical and numerical modelling and it suggests that the technical constraints to making this phenomenon more widely available can be dramatically relaxed.
We realize a quantum-compatible multimode interaction in an ultrahigh Q mechanical resonator via a reservoir-mediated parametric coupling. We use this interaction to demonstrate nondegenerate parametric amplification and thermomechanical noise squeezing, finding excellent agreement with a theoretical model of this interaction over a large dynamic range. This realization of strong multimode nonlinearities in a mechanical platform compatible with quantum-limited optical detection and cooling makes this a powerful system for nonlinear approaches to quantum metrology, transduction between optical and phononic fields, and the quantum manipulation of phononic degrees of freedom.
We discuss the generation of strong stationary mechanical squeezing and entanglement in the modulated two-and three-mode optomechanics. Following the reservoir engineering scheme, the beam-splitter and parametric optomechanical interactions can be simultaneously achieved through appropriately choosing the modulation frequency on mechanical motion, which is essential to strong squeezing and entanglement. In the two-mode modulated optomechanics, squeezing is tunable by the relative ratio of parametric and beam-splitter couplings, and also robust to thermal noise due to the simultaneously optically induced cooling process. In the three-mode modulated optomechanics, strong EPR-type entanglement is also attainable, which can surpass the 3dB limit of nondegenerate parametric interaction. However, the ideal entanglement is impossible since only one of mechanical Bogoliubov modes is cooled by the cavity mode, which also makes the entanglement fragile to the mechanical noise.
Quantum squeezing is an important resource in modern quantum technologies, such as quantum precision measurement and continuous-variable quantum information processing. The generation of squeezed states of mechanical modes is a significant task in cavity optomechanics. Motivated by recent interest in multimode optomechanics, it becomes an interesting topic to create quadrature squeezing in multiple mechanical resonators. However, in the multiple-degenerate-mechanical-mode optomechanical systems, the dark-mode effect strongly suppresses the quantum effects in mechanical modes. Here we study the generation of mechanical squeezing in a two-mechanical-mode optomechanical system by breaking the dark-mode effect with the synthetic-gauge-field method. We find that, when the mechanical modes work at a finite temperature, the mechanical squeezing is weak or even disappears due to the dark-mode effect, while the strong mechanical squeezing can be generated once the dark-mode effect is broken. In particular, the thermal-phonon-occupation tolerance of the mechanical squeezing is approximately three orders of magnitude larger than that without breaking the dark-mode effect. We also generalize this method to break the dark modes and to create the mechanical squeezing in multiple-mechanical-mode optomechanical systems. Our results describe a general physical mechanism and pave the way towards the generation of noise-resistant quantum resources.
Quantum squeezing plays a crucial role in enhancing the precision of quantum metrology and improving the efficiency of quantum information processing protocols. We thus propose a scheme to amplify two-mode squeezing in nanomechanical resonators, harnessing parametric amplification and two-tone laser controls. The red-detuned laser drives facilitate the cooling of the nanomechanical resonators down to their ground state and allow optimal quantum state transfer in the weak-coupling, resolved sideband regime. In particular, the competing blue-detuned lasers in the driving pairs induce displacement squeezing in mechanical resonators. Thus, the quantum state transfer of the squeezing in nanomechanical resonators and the intracavity correlated photons of the parametric amplifier significantly enhance the two-mode mechanical squeezing. Notably, increasing the coupling strength of the red detuned laser and the ratio of blue-to-red detuned laser dramatically amplifies the two-mode mechanical squeezing under realistic experiment parameters of a typical optomechanical system. Our findings reveal that the proposed cooperative mechanism effectively enhances the level of two-mode mechanical squeezing with a considerable improvement and demonstrates exceptional resilience to thermal noise.